JEE Physics · Hard

Fluid Mechanics: Buoyancy MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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BuoyancyHardQuestion 30911

Question

A hollow sphere of outer radius R, inner radius r, and material density ρ_s just floats in water (density ρ_w). The relation is:
  1. A
    ρ_s(R³−r³) = ρ_w R³
    Correct
  2. B
    ρ_s R³ = ρ_w(R³−r³)
  3. C
    ρ_s r³ = ρ_w R³
  4. D
    ρ_s(R³+r³) = ρ_w R³

Correct answer

ρ_s(R³−r³) = ρ_w R³

Explanation

Weight of shell = ρ_s × (4π/3)(R³−r³)g. Buoyant force = ρ_w × (4π/3)R³g. Setting equal: ρ_s(R³−r³) = ρ_w R³.